[EN] In this paper, we propose a general class of fourth-order optimal multi-point methods without
memory for obtaining simple roots. This class requires only three functional evaluations (viz.
two evaluations of function ...[+]

[EN] In this paper, we propose a general class of fourth-order optimal multi-point methods without
memory for obtaining simple roots. This class requires only three functional evaluations (viz.
two evaluations of function f(xn), f(yn) and one of its first-order derivative f
(xn)) per iteration.
Further, we show that the well-known Ostrowski’s method and King’s family of fourth-order
procedures are special cases of our proposed schemes. One of the new particular subclasses
is a biparametric family of iterative methods. By using complex dynamics tools, its stability
is analyzed, showing stable members of the family. Further on, one of the parameters is fixed
and the stability of the resulting class is studied. On the other hand, the accuracy and validity
of new schemes is tested by a number of numerical examples by comparing them with recent
and classical optimal fourth-order methods available in the literature. It is found that they are
very useful in high precision computations.[-]